Browse > Article
http://dx.doi.org/10.4134/CKMS.c200183

SOME CLASSES OF INTEGRAL EQUATIONS OF CONVOLUTIONS-PAIR GENERATED BY THE KONTOROVICH-LEBEDEV, LAPLACE AND FOURIER TRANSFORMS  

Tuan, Trinh (Department of Mathematics Electric Power University)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.3, 2021 , pp. 485-494 More about this Journal
Abstract
In this article, we prove the existence of a solution to some classes of integral equations of generalized convolution type generated by the Kontorovich-Lebedev (K) transform, the Laplace (𝓛) transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.
Keywords
Convolution; Fourier sine; Fourier cosine; Kontorovichh-Lebedev; transform;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. N. Tsitsiklis and B. C. Levy, Integral equations and resolvents of Toeplitz plus Hankel kernels, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology. Series/Report No.: LIDS-P 1170 (1981).
2 U. Grenander and G. Szego, Toeplitz Forms and Their Applications, California Monographs in Mathematical Sciences, University of California Press, Berkeley, 1958.
3 L. X. Huy and N. X. Thao, On the Laplace generalized convolution transform, Ann. Univ. Sci. Budapest. Sect. Comput. 43 (2014), 303-316.
4 J. L. Schiff, The Laplace Transform, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1999. https://doi.org/10.1007/978-0-387-22757-3
5 N. X. Thao, V. K. Tuan, and N. T. Hong,On the Toeplitz plus Hankel integral equations, Int. Trans. & Spec. Funct. 22 (2011), no. 10, 723-737.   DOI
6 N. X. Thao, V. K. Tuan, L. X. Huy, and N. T. Hong, On the Fourier-Laplace convolution transforms, Int. Trans. & Spec Funct. 26 (2015), no. 4, 30313.
7 E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, third edition, Chelsea Publishing Co., New York, 1986.
8 T. Tuan, On the generalized convolution with a weight function for the Fourier cosine and the inverse Kontorovich-Lebedev integral transformations, Nonlinear Funct. Anal. Appl. 12 (2007), no. 2, 325-341.
9 T. Tuan, On the Fourier sine and Kontorovich-Lebedev generalized convolution transforms and applications, Ukrain. Mat. Zh. 72 (2020), no. 2, 267-279. https://doi.org/10.1007/s11253-020-01782-1   DOI
10 T. Tuan and N. T. Hong, A class of Fredholm equations and systems of equations related to the Kontorovich-Lebedev and the Fourier integral transforms, Turkish J. Math. 44 (2020), no. 3, 643-655. https://doi.org/10.3906/mat-2001-24   DOI
11 T. Tuan, N. X. Thao, and N. V. Mau, On the generalized convolution for the Fourier sine and the Kontorovich-Lebedev transforms, Acta Math. Vietnam. 35 (2010), no. 2, 303-317.
12 H. M. Srivastava and R. G. Buschman, Theory and Applications of Convolution Integral Equations, Kluwer Series on Mathematics and Its Applications, Vol. 79. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1992.
13 N. X. Than and T. Tuan, Generalized convolutions of the integral Kontorovich-Lebedev, Fourier sine and cosine transforms, Ann. Univ. Sci. Budapest. Sect. Comput. 25 (2005), 37-51.
14 N. X. Thao, T. Tuan, and L. X. Huy, The Fourier-Laplace generalized convolutions and applications to integral equations, Vietnam J. Math. 41 (2013), no. 4, 451-464. https://doi.org/10.1007/s10013-013-0044-0   DOI
15 T. Tuan, P. V. Hoang, and N. T. Hong, Integral equation of Toeplitz plus Hankel's type and parabolic equation related to the Kontorovich-Lebedev-Fourier generalized convolutions, Math. Methods Appl. Sci. 41 (2018), no. 17, 8171-8181. https://doi.org/10.1002/mma.5279   DOI
16 S. B. Yakubovich, Index Transforms, World Scientific Publishing Co., Inc., River Edge, NJ, 1996. https://doi.org/10.1142/9789812831064
17 N. Mikaeilvand and S. Noeiaghdam, Mean value theorem for integrals and its application on numerically solving of Fredholm integral equation of second kind with Toeplitz plus Hankel Kernel, Int. J. Industrial Math. 6 (2014), no. 4, 351-360.
18 N. X. Thao, V. K. Tuan, and H. T. V. Anh, On the Toeplitz plus Hankel integral equation II, Int. Trans. & Spec. Funct. 25 (2014), no. 1, 75-84.   DOI
19 A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms. Vol. II, McGraw-Hill Book Company, Inc., New York, 1954.